A big player in downtown Miami development has solidified plans to build a major, privately financed convention center topped by a massive, 1,800-room hotel — the largest in South Florida — on the site of the demolished Miami Arena.

MDM Group confirmed Thursday it has a contract to purchase the old arena site from the developers of the larger Miami World Center, a long-planned mixed-use project that would take up several blocks in the Park West district west of Biscayne Boulevard downtown. Terms were not disclosed.

MDM and its architects also released a rendering and a video, posted on You Tube, of a swooping, cascading, three-legged Marriott hotel tower rising over a huge podium containing the 500,000-square-foot convention center, a 1,500-seat theater, and a 2,300-car garage partly buried under ground.

As news of the project, which had been rumored for months, trickled out this week, MDM and Miami World Center principals have declined to elaborate in detail on the massive plan’s cost, financing plans or timetable. No plans have been submitted to the city of Miami, where officials — who have long urged development of a new downtown convention center — say they have not been approached by the developers.

But MDM’s architect, John Nichols, who was authorized to speak on the developers’ behalf, said his client intends to push forward quickly, believes it’s financially feasible because of high demand for hotels and meeting space in Miami, and could have the project done within four years. Nichols said the project would easily cost more than $1 billion.

“Miami is such a red-hot community, and this will be a true iconic landmark on the horizon,’’ said Nichols, of Nichols Brosch Wurst Wolfe, who said the firm has completed a conceptual design. “This is a huge undertaking. We’ve blocked it out and we know it will work.’’

At the same time, Miami World Center, whose ambitious plans were stalled by the real-estate crash, appears ready to move ahead with a large retail center and several residential buildings next to the contemplated convention center. The company has issued marketing materials outlining 1 million square feet of retail, restaurant and entertainment space.

Nichols said MDM and Miami World Center are closely coordinating planning and design to ensure the project meets the goals of the broader development, which was approved as a special zoning district by the city during the previous real-estate boom. That plan outlined a dense, pedestrian-friendly district that mixes retail, commercial and residential buildings of different scales with open spaces to ensure an urban neighborhood feel.

Nichols said MDM — which separately is completing the four-block Met Miami mega-project downtown — intends to raise all financing for the project privately, with no publicmoney. Marriott has agreed to manage the hotel, Nichols said, though the company would not comment Thursday.

Because the site sits within the city’s Overtown/Park West Community Redevelopment Agency area, however, both the convention center and the Miami World Center projects could qualify for public money from the special taxing district — possibly in the form of tax rebates — to improve public infrastructure, from sewer lines to streets and sidewalks.

The convention center plan was given additional impetus by Florida East Coast’s plans to build a massive train station across the street for its planned All Aboard Florida rail service, which will connect downtown Miami to Orlando. The convention center and hotel would be linked directly to the train station and the Overtown Metrorail station through sky bridges, Nichols said.

“We’re tying all of it together. You will be able to flow through and around this (convention center) facility and right into the station,’’ he said.

The confirmation of MDM’s plans comes as Miami Beach is in the final phases of selecting a team to modernize and expand its aging convention center, add an 800-room hotel and redevelop the site with residential buildings, cultural facilities and park space.

It’s unclear how the Miami convention center would affect the Beach redevelopment plans. The proposed convention center in Miami, with just 100,000 square feet of convention floor space — much of its square footage will be for ballrooms and meeting rooms — is significantly smaller than its Beach counterpart, though the Miami hotel would be more than twice as large.

Nichols said the Miami convention hotel would have substantial, resort-like amenities, including an expansive pool deck with views of the bay, the American Airlines Arena and the downtown skyline. The facility would also boast an 80,000-square-foot outdoor event deck. The structure would rise 58 stories, he said.

During final presentations this week, the leader of one of two development-and-design teams vying for the $1 billion-plus Beach project, New York builder and hotel developer Dan Tishman, said the main competition for the Beach convention center hotel would be similar facilities across the bay in downtown Miami. A spokesman for the team said Thursday that Tishman also warned Beach officials that their convention center could lose significant business if it’s not improved, especially in the face of growing competition.

A spokesman for the competing team, Portman-CMC, said the group did not want to comment on the Miami convention project.

Miami City Commission Chairman Marc Sarnoff, also chairman of the Downtown Development Authority, said the contemplated center would not affect the Beach’s project nor the city-owned Knight Center on the Miami River, which is substantially smaller. Sarnoff said he was unfamiliar with the particulars of the plan, though he knew of the effort and applauds it.

“We’ve always wanted a convention center, but people don’t want to spend money on a private convention center,’’ Sarnoff said. “Kudos to them.’’

Nichols said MDM’s principals believe their convention center would supplement the larger Beach facility, not compete with it. Because of its smaller size, the Miami center could not accommodate the major conventions and shows the Beach aims to attract.

“It’s going after a different market,’’ Nichols said. “They have been working diligently on this for some time, and it doesn’t have a thing to do with what’s going on in Miami Beach. This is about downtown Miami.’’